The present invention relates to a road vehicle power assisted steering system and is particularly concerned with a system in which power assistance to displacement of a steering component of a steering gear assembly is provided by actuation of electric motor means. Such a steering system is generally known from U.S. Pat. No. 4,415,054. This latter U.S. Patent discloses a rack and pinion steering gear assembly in which permanent magnets of an electric motor are incorporated in a rack bar housing; rotor coils or windings of the motor are rotatably mounted in the rack bar housing to rotate with a ball nut that is longitudinally restrained relative to the rack bar and engages with a screw threaded portion of the rack bar so that, when an electric current is applied to the motor, the ball nut is caused to rotate and drive the rack bar longitudinally with a force which is related to the magnitude of the applied current and in a direction dependent upon the polarity of the applied current to provide the required power assistance to displacement of the rack bar. The magnitude and polarity of the current which is applied to the motor is controlled in response to the magnitude and direction of a steering torque which is applied to the rack and pinion gear through the pinion. With such a known system, it is readily appreciated that during a steering manoeuvre a substantial amount of kinetic energy will be developed by the movement of the rack bar, the rotor/ball nut and other displaceable parts of the steering gear assembly. This kinetic energy, if not rapidly dissipated from the steering system at the end of an applied torque sequence for a particular steering manoeuvre, can cause the displaceable steering component of the gear assembly to over-shoot or over-steer with consequential adverse effects on the steering characteristics of the system. A possible means of alleviating this problem is to dampen the steering system, for example by increasing the resistance or friction to displacement of the components in the gear assembly, this however is considered unacceptable since the high levels of friction necessary to provide adequate damping would make the steering system harder to operate, would increase wear, and would require a more powerful electric motor which would result in greater expense and size of the system and be a greater drain on the power output of the road vehicle. It is an object of the present invention to provide an electric power assisted steering system for a road vehicle which provides an efficient, simple and economical means of alleviating the problems associated with over-steering or over-shooting of the displaceable components of the steering gear assembly as discussed above.